Problem: $\dfrac{5}{4} \div \dfrac{6}{7} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{6}{7}$ is $\dfrac{7}{6}$ Therefore: $ \dfrac{5}{4} \div \dfrac{6}{7} = \dfrac{5}{4} \times \dfrac{7}{6} $ $ \phantom{\dfrac{5}{4} \times \dfrac{7}{6}} = \dfrac{5 \times 7}{4 \times 6} $ $ \phantom{\dfrac{5}{4} \times \dfrac{7}{6}} = \dfrac{35}{24} $